A bolt is to be made 2.0 cm long with a tolerance of 4%. Set up an equation to solve for the shortest and longest bolt length. S
1 answer:
Answer:
The equations are:
Step-by-step explanation:
The ideal length of the bolt is 2.0 cm, since it has a tolerance of 4%, this means that length values between and
are acceptable, because by those expressions the length of the bolt will be 4% higher or lower than it's original length. With this in mind let's find it's values:
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Answer:
a.
With n = 25,
With n = 50,
b.
c.
The absolute error in the trapezoid rule is 0.08047
The absolute error in the Simpson's rule is 0.00008
Step-by-step explanation:
a. To approximate the integral using n = 25 with the trapezoid rule you must:
The trapezoidal rule states that
where
We have that a = 0, b = 1, n = 25.
Therefore,
We need to divide the interval [0,1] into n = 25 sub-intervals of length , with the following endpoints:
Now, we just evaluate the function at these endpoints:
...
Applying the trapezoid rule formula we get
- To approximate the integral
using n = 50 with the trapezoid rule you must:
We have that a = 0, b = 1, n = 50.
Therefore,
We need to divide the interval [0,1] into n = 50 sub-intervals of length , with the following endpoints:
Now, we just evaluate the function at these endpoints:
...
Applying the trapezoid rule formula we get
b. To approximate the integral using 2n with the Simpson's rule you must:
The Simpson's rule states that
where
We have that a = 0, b = 1, n = 50
Therefore,
We need to divide the interval [0,1] into n = 50 sub-intervals of length , with the following endpoints:
Now, we just evaluate the function at these endpoints:
...
Applying the Simpson's rule formula we get
c. If B is our estimate of some quantity having an actual value of A, then the absolute error is given by
The absolute error in the trapezoid rule is
The calculated value is
and our estimate is 67.1519320308594
Thus, the absolute error is given by
The absolute error in the Simpson's rule is